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glibc/sysdeps/ia64/fpu/libm_lgammaf.S
Siddhesh Poyarekar 30891f35fa Remove "Contributed by" lines 
We stopped adding "Contributed by" or similar lines in sources in 2012
in favour of git logs and keeping the Contributors section of the
glibc manual up to date.  Removing these lines makes the license
header a bit more consistent across files and also removes the
possibility of error in attribution when license blocks or files are
copied across since the contributed-by lines don't actually reflect
reality in those cases.

Move all "Contributed by" and similar lines (Written by, Test by,
etc.) into a new file CONTRIBUTED-BY to retain record of these
contributions.  These contributors are also mentioned in
manual/contrib.texi, so we just maintain this additional record as a
courtesy to the earlier developers.

The following scripts were used to filter a list of files to edit in
place and to clean up the CONTRIBUTED-BY file respectively.  These
were not added to the glibc sources because they're not expected to be
of any use in future given that this is a one time task:

https://gist.github.com/siddhesh/b5ecac94eabfd72ed2916d6d8157e7dc
https://gist.github.com/siddhesh/15ea1f5e435ace9774f485030695ee02

Reviewed-by: Carlos O'Donell <carlos@redhat.com>
2021-09-03 22:06:44 +05:30

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.file "libm_lgammaf.s"
// Copyright (c) 2002 - 2005, Intel Corporation
// All rights reserved.
//
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// * The name of Intel Corporation may not be used to endorse or promote
// products derived from this software without specific prior written
// permission.
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,INCLUDING,BUT NOT
// LIMITED TO,THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT,INDIRECT,INCIDENTAL,SPECIAL,
// EXEMPLARY,OR CONSEQUENTIAL DAMAGES (INCLUDING,BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,DATA,OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
// OF LIABILITY,WHETHER IN CONTRACT,STRICT LIABILITY OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE,EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Intel Corporation is the author of this code,and requests that all
// problem reports or change requests be submitted to it directly at
// http://www.intel.com/software/products/opensource/libraries/num.htm.
//
//*********************************************************************
//
// History:
// 01/10/02 Initial version
// 01/25/02 Corrected parameter store, load, and tag for __libm_error_support
// 02/01/02 Added support of SIGN(GAMMA(x)) calculation
// 05/20/02 Cleaned up namespace and sf0 syntax
// 09/16/02 Improved accuracy on intervals reduced to [1;1.25]
// 10/21/02 Now it returns SIGN(GAMMA(x))=-1 for negative zero
// 02/10/03 Reordered header: .section, .global, .proc, .align
// 07/22/03 Reformatted some data tables
// 03/31/05 Reformatted delimiters between data tables
//
//*********************************************************************
//
//*********************************************************************
//
// Function: __libm_lgammaf(float x, int* signgam, int szsigngam)
// computes the principle value of the logarithm of the GAMMA function
// of x. Signum of GAMMA(x) is stored to memory starting at the address
// specified by the signgam.
//
//*********************************************************************
//
// Resources Used:
//
// Floating-Point Registers: f6-f15
// f32-f97
//
// General Purpose Registers:
// r8-r11
// r14-r30
// r32-r36
// r37-r40 (Used to pass arguments to error handling routine)
//
// Predicate Registers: p6-p15
//
//*********************************************************************
//
// IEEE Special Conditions:
//
// lgamma(+inf) = +inf
// lgamma(-inf) = +inf
// lgamma(+/-0) = +inf
// lgamma(x<0, x - integer) = +inf
// lgamma(SNaN) = QNaN
// lgamma(QNaN) = QNaN
//
//*********************************************************************
//
// Overview
//
// The method consists of three cases.
//
// If 2^13 <= x < OVERFLOW_BOUNDARY use case lgammaf_pstirling;
// else if 1 < x < 2^13 use case lgammaf_regular;
// else if -9 < x < 1 use case lgammaf_negrecursion;
// else if -2^13 < x < -9 use case lgammaf_negpoly;
// else if x < -2^13 use case lgammaf_negstirling;
// else if x is close to negative
// roots of ln(GAMMA(x)) use case lgammaf_negroots;
//
//
// Case 2^13 <= x < OVERFLOW_BOUNDARY
// ----------------------------------
// Here we use algorithm based on the Stirling formula:
// ln(GAMMA(x)) = ln(sqrt(2*Pi)) + (x-0.5)*ln(x) - x
//
// Case 1 < x < 2^13
// -----------------
// To calculate ln(GAMMA(x)) for such arguments we use polynomial
// approximation on following intervals: [1.0; 1.25), [1.25; 1.5),
// [1.5, 1.75), [1.75; 2), [2; 4), [2^i; 2^(i+1)), i=1..8
//
// Following variants of approximation and argument reduction are used:
// 1. [1.0; 1.25)
// ln(GAMMA(x)) ~ (x-1.0)*P7(x)
//
// 2. [1.25; 1.5)
// ln(GAMMA(x)) ~ ln(GAMMA(x0))+(x-x0)*P8(x-x0),
// where x0 - point of local minimum on [1;2] rounded to nearest double
// precision number.
//
// 3. [1.5; 1.75)
// ln(GAMMA(x)) ~ P8(x)
//
// 4. [1.75; 2.0)
// ln(GAMMA(x)) ~ (x-2)*P7(x)
//
// 5. [2; 4)
// ln(GAMMA(x)) ~ (x-2)*P10(x)
//
// 6. [2^i; 2^(i+1)), i=2..8
// ln(GAMMA(x)) ~ P10((x-2^i)/2^i)
//
// Case -9 < x < 1
// ---------------
// Here we use the recursive formula:
// ln(GAMMA(x)) = ln(GAMMA(x+1)) - ln(x)
//
// Using this formula we reduce argument to base interval [1.0; 2.0]
//
// Case -2^13 < x < -9
// --------------------
// Here we use the formula:
// ln(GAMMA(x)) = ln(Pi/(|x|*GAMMA(|x|)*sin(Pi*|x|))) =
// = -ln(|x|) - ln((GAMMA(|x|)) - ln(sin(Pi*r)/(Pi*r)) - ln(|r|)
// where r = x - rounded_to_nearest(x), i.e |r| <= 0.5 and
// ln(sin(Pi*r)/(Pi*r)) is approximated by 8-degree polynomial of r^2
//
// Case x < -2^13
// --------------
// Here we use algorithm based on the Stirling formula:
// ln(GAMMA(x)) = -ln(sqrt(2*Pi)) + (|x|-0.5)ln(x) - |x| -
// - ln(sin(Pi*r)/(Pi*r)) - ln(|r|)
// where r = x - rounded_to_nearest(x).
//
// Neighbourhoods of negative roots
// --------------------------------
// Here we use polynomial approximation
// ln(GAMMA(x-x0)) = ln(GAMMA(x0)) + (x-x0)*P14(x-x0),
// where x0 is a root of ln(GAMMA(x)) rounded to nearest double
// precision number.
//
//
// Claculation of logarithm
// ------------------------
// Consider x = 2^N * xf so
// ln(x) = ln(frcpa(x)*x/frcpa(x))
// = ln(1/frcpa(x)) + ln(frcpa(x)*x)
//
// frcpa(x) = 2^(-N) * frcpa(xf)
//
// ln(1/frcpa(x)) = -ln(2^(-N)) - ln(frcpa(xf))
// = N*ln(2) - ln(frcpa(xf))
// = N*ln(2) + ln(1/frcpa(xf))
//
// ln(x) = ln(1/frcpa(x)) + ln(frcpa(x)*x) =
// = N*ln(2) + ln(1/frcpa(xf)) + ln(frcpa(x)*x)
// = N*ln(2) + T + ln(frcpa(x)*x)
//
// Let r = 1 - frcpa(x)*x, note that r is quite small by
// absolute value so
//
// ln(x) = N*ln(2) + T + ln(1+r) ~ N*ln(2) + T + Series(r),
// where T - is precomputed tabular value,
// Series(r) = (P3*r + P2)*r^2 + (P1*r + 1)
//
//*********************************************************************
GR_TAG = r8
GR_ad_Data = r8
GR_ad_Co = r9
GR_ad_SignGam = r10
GR_ad_Ce = r10
GR_SignExp = r11
GR_ad_C650 = r14
GR_ad_RootCo = r14
GR_ad_C0 = r15
GR_Dx = r15
GR_Ind = r16
GR_Offs = r17
GR_IntNum = r17
GR_ExpBias = r18
GR_ExpMask = r19
GR_Ind4T = r20
GR_RootInd = r20
GR_Sig = r21
GR_Exp = r22
GR_PureExp = r23
GR_ad_C43 = r24
GR_StirlBound = r25
GR_ad_T = r25
GR_IndX8 = r25
GR_Neg2 = r25
GR_2xDx = r25
GR_SingBound = r26
GR_IndX2 = r26
GR_Neg4 = r26
GR_ad_RootCe = r26
GR_Arg = r27
GR_ExpOf2 = r28
GR_fff7 = r28
GR_Root = r28
GR_ReqBound = r28
GR_N = r29
GR_ad_Root = r30
GR_ad_OvfBound = r30
GR_SignOfGamma = r31
GR_SAVE_B0 = r33
GR_SAVE_PFS = r34
GR_SAVE_GP = r35
GR_SAVE_SP = r36
GR_Parameter_X = r37
GR_Parameter_Y = r38
GR_Parameter_RESULT = r39
GR_Parameter_TAG = r40
//*********************************************************************
FR_X = f10
FR_Y = f1 // lgammaf is single argument function
FR_RESULT = f8
FR_x = f6
FR_x2 = f7
FR_x3 = f9
FR_x4 = f10
FR_xm2 = f11
FR_w = f11
FR_w2 = f12
FR_Q32 = f13
FR_Q10 = f14
FR_InvX = f15
FR_NormX = f32
FR_A0 = f33
FR_A1 = f34
FR_A2 = f35
FR_A3 = f36
FR_A4 = f37
FR_A5 = f38
FR_A6 = f39
FR_A7 = f40
FR_A8 = f41
FR_A9 = f42
FR_A10 = f43
FR_int_N = f44
FR_P3 = f45
FR_P2 = f46
FR_P1 = f47
FR_LocalMin = f48
FR_Ln2 = f49
FR_05 = f50
FR_LnSqrt2Pi = f51
FR_3 = f52
FR_r = f53
FR_r2 = f54
FR_T = f55
FR_N = f56
FR_xm05 = f57
FR_int_Ln = f58
FR_P32 = f59
FR_P10 = f60
FR_Xf = f61
FR_InvXf = f62
FR_rf = f63
FR_rf2 = f64
FR_Tf = f65
FR_Nf = f66
FR_xm05f = f67
FR_P32f = f68
FR_P10f = f69
FR_Lnf = f70
FR_Xf2 = f71
FR_Xf4 = f72
FR_Xf8 = f73
FR_Ln = f74
FR_xx = f75
FR_Root = f75
FR_Req = f76
FR_1pXf = f77
FR_S16 = f78
FR_R3 = f78
FR_S14 = f79
FR_R2 = f79
FR_S12 = f80
FR_R1 = f80
FR_S10 = f81
FR_R0 = f81
FR_S8 = f82
FR_rx = f82
FR_S6 = f83
FR_rx2 = f84
FR_S4 = f84
FR_S2 = f85
FR_Xp1 = f86
FR_Xp2 = f87
FR_Xp3 = f88
FR_Xp4 = f89
FR_Xp5 = f90
FR_Xp6 = f91
FR_Xp7 = f92
FR_Xp8 = f93
FR_OverflowBound = f93
FR_2 = f94
FR_tmp = f95
FR_int_Ntrunc = f96
FR_Ntrunc = f97
//*********************************************************************
RODATA
.align 32
LOCAL_OBJECT_START(lgammaf_data)
log_table_1:
data8 0xbfd0001008f39d59 // P3
data8 0x3fd5556073e0c45a // P2
data8 0x3fe62e42fefa39ef // ln(2)
data8 0x3fe0000000000000 // 0.5
//
data8 0x3F60040155D5889E //ln(1/frcpa(1+ 0/256)
data8 0x3F78121214586B54 //ln(1/frcpa(1+ 1/256)
data8 0x3F841929F96832F0 //ln(1/frcpa(1+ 2/256)
data8 0x3F8C317384C75F06 //ln(1/frcpa(1+ 3/256)
data8 0x3F91A6B91AC73386 //ln(1/frcpa(1+ 4/256)
data8 0x3F95BA9A5D9AC039 //ln(1/frcpa(1+ 5/256)
data8 0x3F99D2A8074325F4 //ln(1/frcpa(1+ 6/256)
data8 0x3F9D6B2725979802 //ln(1/frcpa(1+ 7/256)
data8 0x3FA0C58FA19DFAAA //ln(1/frcpa(1+ 8/256)
data8 0x3FA2954C78CBCE1B //ln(1/frcpa(1+ 9/256)
data8 0x3FA4A94D2DA96C56 //ln(1/frcpa(1+ 10/256)
data8 0x3FA67C94F2D4BB58 //ln(1/frcpa(1+ 11/256)
data8 0x3FA85188B630F068 //ln(1/frcpa(1+ 12/256)
data8 0x3FAA6B8ABE73AF4C //ln(1/frcpa(1+ 13/256)
data8 0x3FAC441E06F72A9E //ln(1/frcpa(1+ 14/256)
data8 0x3FAE1E6713606D07 //ln(1/frcpa(1+ 15/256)
data8 0x3FAFFA6911AB9301 //ln(1/frcpa(1+ 16/256)
data8 0x3FB0EC139C5DA601 //ln(1/frcpa(1+ 17/256)
data8 0x3FB1DBD2643D190B //ln(1/frcpa(1+ 18/256)
data8 0x3FB2CC7284FE5F1C //ln(1/frcpa(1+ 19/256)
data8 0x3FB3BDF5A7D1EE64 //ln(1/frcpa(1+ 20/256)
data8 0x3FB4B05D7AA012E0 //ln(1/frcpa(1+ 21/256)
data8 0x3FB580DB7CEB5702 //ln(1/frcpa(1+ 22/256)
data8 0x3FB674F089365A7A //ln(1/frcpa(1+ 23/256)
data8 0x3FB769EF2C6B568D //ln(1/frcpa(1+ 24/256)
data8 0x3FB85FD927506A48 //ln(1/frcpa(1+ 25/256)
data8 0x3FB9335E5D594989 //ln(1/frcpa(1+ 26/256)
data8 0x3FBA2B0220C8E5F5 //ln(1/frcpa(1+ 27/256)
data8 0x3FBB0004AC1A86AC //ln(1/frcpa(1+ 28/256)
data8 0x3FBBF968769FCA11 //ln(1/frcpa(1+ 29/256)
data8 0x3FBCCFEDBFEE13A8 //ln(1/frcpa(1+ 30/256)
data8 0x3FBDA727638446A2 //ln(1/frcpa(1+ 31/256)
data8 0x3FBEA3257FE10F7A //ln(1/frcpa(1+ 32/256)
data8 0x3FBF7BE9FEDBFDE6 //ln(1/frcpa(1+ 33/256)
data8 0x3FC02AB352FF25F4 //ln(1/frcpa(1+ 34/256)
data8 0x3FC097CE579D204D //ln(1/frcpa(1+ 35/256)
data8 0x3FC1178E8227E47C //ln(1/frcpa(1+ 36/256)
data8 0x3FC185747DBECF34 //ln(1/frcpa(1+ 37/256)
data8 0x3FC1F3B925F25D41 //ln(1/frcpa(1+ 38/256)
data8 0x3FC2625D1E6DDF57 //ln(1/frcpa(1+ 39/256)
data8 0x3FC2D1610C86813A //ln(1/frcpa(1+ 40/256)
data8 0x3FC340C59741142E //ln(1/frcpa(1+ 41/256)
data8 0x3FC3B08B6757F2A9 //ln(1/frcpa(1+ 42/256)
data8 0x3FC40DFB08378003 //ln(1/frcpa(1+ 43/256)
data8 0x3FC47E74E8CA5F7C //ln(1/frcpa(1+ 44/256)
data8 0x3FC4EF51F6466DE4 //ln(1/frcpa(1+ 45/256)
data8 0x3FC56092E02BA516 //ln(1/frcpa(1+ 46/256)
data8 0x3FC5D23857CD74D5 //ln(1/frcpa(1+ 47/256)
data8 0x3FC6313A37335D76 //ln(1/frcpa(1+ 48/256)
data8 0x3FC6A399DABBD383 //ln(1/frcpa(1+ 49/256)
data8 0x3FC70337DD3CE41B //ln(1/frcpa(1+ 50/256)
data8 0x3FC77654128F6127 //ln(1/frcpa(1+ 51/256)
data8 0x3FC7E9D82A0B022D //ln(1/frcpa(1+ 52/256)
data8 0x3FC84A6B759F512F //ln(1/frcpa(1+ 53/256)
data8 0x3FC8AB47D5F5A310 //ln(1/frcpa(1+ 54/256)
data8 0x3FC91FE49096581B //ln(1/frcpa(1+ 55/256)
data8 0x3FC981634011AA75 //ln(1/frcpa(1+ 56/256)
data8 0x3FC9F6C407089664 //ln(1/frcpa(1+ 57/256)
data8 0x3FCA58E729348F43 //ln(1/frcpa(1+ 58/256)
data8 0x3FCABB55C31693AD //ln(1/frcpa(1+ 59/256)
data8 0x3FCB1E104919EFD0 //ln(1/frcpa(1+ 60/256)
data8 0x3FCB94EE93E367CB //ln(1/frcpa(1+ 61/256)
data8 0x3FCBF851C067555F //ln(1/frcpa(1+ 62/256)
data8 0x3FCC5C0254BF23A6 //ln(1/frcpa(1+ 63/256)
data8 0x3FCCC000C9DB3C52 //ln(1/frcpa(1+ 64/256)
data8 0x3FCD244D99C85674 //ln(1/frcpa(1+ 65/256)
data8 0x3FCD88E93FB2F450 //ln(1/frcpa(1+ 66/256)
data8 0x3FCDEDD437EAEF01 //ln(1/frcpa(1+ 67/256)
data8 0x3FCE530EFFE71012 //ln(1/frcpa(1+ 68/256)
data8 0x3FCEB89A1648B971 //ln(1/frcpa(1+ 69/256)
data8 0x3FCF1E75FADF9BDE //ln(1/frcpa(1+ 70/256)
data8 0x3FCF84A32EAD7C35 //ln(1/frcpa(1+ 71/256)
data8 0x3FCFEB2233EA07CD //ln(1/frcpa(1+ 72/256)
data8 0x3FD028F9C7035C1C //ln(1/frcpa(1+ 73/256)
data8 0x3FD05C8BE0D9635A //ln(1/frcpa(1+ 74/256)
data8 0x3FD085EB8F8AE797 //ln(1/frcpa(1+ 75/256)
data8 0x3FD0B9C8E32D1911 //ln(1/frcpa(1+ 76/256)
data8 0x3FD0EDD060B78081 //ln(1/frcpa(1+ 77/256)
data8 0x3FD122024CF0063F //ln(1/frcpa(1+ 78/256)
data8 0x3FD14BE2927AECD4 //ln(1/frcpa(1+ 79/256)
data8 0x3FD180618EF18ADF //ln(1/frcpa(1+ 80/256)
data8 0x3FD1B50BBE2FC63B //ln(1/frcpa(1+ 81/256)
data8 0x3FD1DF4CC7CF242D //ln(1/frcpa(1+ 82/256)
data8 0x3FD214456D0EB8D4 //ln(1/frcpa(1+ 83/256)
data8 0x3FD23EC5991EBA49 //ln(1/frcpa(1+ 84/256)
data8 0x3FD2740D9F870AFB //ln(1/frcpa(1+ 85/256)
data8 0x3FD29ECDABCDFA04 //ln(1/frcpa(1+ 86/256)
data8 0x3FD2D46602ADCCEE //ln(1/frcpa(1+ 87/256)
data8 0x3FD2FF66B04EA9D4 //ln(1/frcpa(1+ 88/256)
data8 0x3FD335504B355A37 //ln(1/frcpa(1+ 89/256)
data8 0x3FD360925EC44F5D //ln(1/frcpa(1+ 90/256)
data8 0x3FD38BF1C3337E75 //ln(1/frcpa(1+ 91/256)
data8 0x3FD3C25277333184 //ln(1/frcpa(1+ 92/256)
data8 0x3FD3EDF463C1683E //ln(1/frcpa(1+ 93/256)
data8 0x3FD419B423D5E8C7 //ln(1/frcpa(1+ 94/256)
data8 0x3FD44591E0539F49 //ln(1/frcpa(1+ 95/256)
data8 0x3FD47C9175B6F0AD //ln(1/frcpa(1+ 96/256)
data8 0x3FD4A8B341552B09 //ln(1/frcpa(1+ 97/256)
data8 0x3FD4D4F3908901A0 //ln(1/frcpa(1+ 98/256)
data8 0x3FD501528DA1F968 //ln(1/frcpa(1+ 99/256)
data8 0x3FD52DD06347D4F6 //ln(1/frcpa(1+ 100/256)
data8 0x3FD55A6D3C7B8A8A //ln(1/frcpa(1+ 101/256)
data8 0x3FD5925D2B112A59 //ln(1/frcpa(1+ 102/256)
data8 0x3FD5BF406B543DB2 //ln(1/frcpa(1+ 103/256)
data8 0x3FD5EC433D5C35AE //ln(1/frcpa(1+ 104/256)
data8 0x3FD61965CDB02C1F //ln(1/frcpa(1+ 105/256)
data8 0x3FD646A84935B2A2 //ln(1/frcpa(1+ 106/256)
data8 0x3FD6740ADD31DE94 //ln(1/frcpa(1+ 107/256)
data8 0x3FD6A18DB74A58C5 //ln(1/frcpa(1+ 108/256)
data8 0x3FD6CF31058670EC //ln(1/frcpa(1+ 109/256)
data8 0x3FD6F180E852F0BA //ln(1/frcpa(1+ 110/256)
data8 0x3FD71F5D71B894F0 //ln(1/frcpa(1+ 111/256)
data8 0x3FD74D5AEFD66D5C //ln(1/frcpa(1+ 112/256)
data8 0x3FD77B79922BD37E //ln(1/frcpa(1+ 113/256)
data8 0x3FD7A9B9889F19E2 //ln(1/frcpa(1+ 114/256)
data8 0x3FD7D81B037EB6A6 //ln(1/frcpa(1+ 115/256)
data8 0x3FD8069E33827231 //ln(1/frcpa(1+ 116/256)
data8 0x3FD82996D3EF8BCB //ln(1/frcpa(1+ 117/256)
data8 0x3FD85855776DCBFB //ln(1/frcpa(1+ 118/256)
data8 0x3FD8873658327CCF //ln(1/frcpa(1+ 119/256)
data8 0x3FD8AA75973AB8CF //ln(1/frcpa(1+ 120/256)
data8 0x3FD8D992DC8824E5 //ln(1/frcpa(1+ 121/256)
data8 0x3FD908D2EA7D9512 //ln(1/frcpa(1+ 122/256)
data8 0x3FD92C59E79C0E56 //ln(1/frcpa(1+ 123/256)
data8 0x3FD95BD750EE3ED3 //ln(1/frcpa(1+ 124/256)
data8 0x3FD98B7811A3EE5B //ln(1/frcpa(1+ 125/256)
data8 0x3FD9AF47F33D406C //ln(1/frcpa(1+ 126/256)
data8 0x3FD9DF270C1914A8 //ln(1/frcpa(1+ 127/256)
data8 0x3FDA0325ED14FDA4 //ln(1/frcpa(1+ 128/256)
data8 0x3FDA33440224FA79 //ln(1/frcpa(1+ 129/256)
data8 0x3FDA57725E80C383 //ln(1/frcpa(1+ 130/256)
data8 0x3FDA87D0165DD199 //ln(1/frcpa(1+ 131/256)
data8 0x3FDAAC2E6C03F896 //ln(1/frcpa(1+ 132/256)
data8 0x3FDADCCC6FDF6A81 //ln(1/frcpa(1+ 133/256)
data8 0x3FDB015B3EB1E790 //ln(1/frcpa(1+ 134/256)
data8 0x3FDB323A3A635948 //ln(1/frcpa(1+ 135/256)
data8 0x3FDB56FA04462909 //ln(1/frcpa(1+ 136/256)
data8 0x3FDB881AA659BC93 //ln(1/frcpa(1+ 137/256)
data8 0x3FDBAD0BEF3DB165 //ln(1/frcpa(1+ 138/256)
data8 0x3FDBD21297781C2F //ln(1/frcpa(1+ 139/256)
data8 0x3FDC039236F08819 //ln(1/frcpa(1+ 140/256)
data8 0x3FDC28CB1E4D32FD //ln(1/frcpa(1+ 141/256)
data8 0x3FDC4E19B84723C2 //ln(1/frcpa(1+ 142/256)
data8 0x3FDC7FF9C74554C9 //ln(1/frcpa(1+ 143/256)
data8 0x3FDCA57B64E9DB05 //ln(1/frcpa(1+ 144/256)
data8 0x3FDCCB130A5CEBB0 //ln(1/frcpa(1+ 145/256)
data8 0x3FDCF0C0D18F326F //ln(1/frcpa(1+ 146/256)
data8 0x3FDD232075B5A201 //ln(1/frcpa(1+ 147/256)
data8 0x3FDD490246DEFA6B //ln(1/frcpa(1+ 148/256)
data8 0x3FDD6EFA918D25CD //ln(1/frcpa(1+ 149/256)
data8 0x3FDD9509707AE52F //ln(1/frcpa(1+ 150/256)
data8 0x3FDDBB2EFE92C554 //ln(1/frcpa(1+ 151/256)
data8 0x3FDDEE2F3445E4AF //ln(1/frcpa(1+ 152/256)
data8 0x3FDE148A1A2726CE //ln(1/frcpa(1+ 153/256)
data8 0x3FDE3AFC0A49FF40 //ln(1/frcpa(1+ 154/256)
data8 0x3FDE6185206D516E //ln(1/frcpa(1+ 155/256)
data8 0x3FDE882578823D52 //ln(1/frcpa(1+ 156/256)
data8 0x3FDEAEDD2EAC990C //ln(1/frcpa(1+ 157/256)
data8 0x3FDED5AC5F436BE3 //ln(1/frcpa(1+ 158/256)
data8 0x3FDEFC9326D16AB9 //ln(1/frcpa(1+ 159/256)
data8 0x3FDF2391A2157600 //ln(1/frcpa(1+ 160/256)
data8 0x3FDF4AA7EE03192D //ln(1/frcpa(1+ 161/256)
data8 0x3FDF71D627C30BB0 //ln(1/frcpa(1+ 162/256)
data8 0x3FDF991C6CB3B379 //ln(1/frcpa(1+ 163/256)
data8 0x3FDFC07ADA69A910 //ln(1/frcpa(1+ 164/256)
data8 0x3FDFE7F18EB03D3E //ln(1/frcpa(1+ 165/256)
data8 0x3FE007C053C5002E //ln(1/frcpa(1+ 166/256)
data8 0x3FE01B942198A5A1 //ln(1/frcpa(1+ 167/256)
data8 0x3FE02F74400C64EB //ln(1/frcpa(1+ 168/256)
data8 0x3FE04360BE7603AD //ln(1/frcpa(1+ 169/256)
data8 0x3FE05759AC47FE34 //ln(1/frcpa(1+ 170/256)
data8 0x3FE06B5F1911CF52 //ln(1/frcpa(1+ 171/256)
data8 0x3FE078BF0533C568 //ln(1/frcpa(1+ 172/256)
data8 0x3FE08CD9687E7B0E //ln(1/frcpa(1+ 173/256)
data8 0x3FE0A10074CF9019 //ln(1/frcpa(1+ 174/256)
data8 0x3FE0B5343A234477 //ln(1/frcpa(1+ 175/256)
data8 0x3FE0C974C89431CE //ln(1/frcpa(1+ 176/256)
data8 0x3FE0DDC2305B9886 //ln(1/frcpa(1+ 177/256)
data8 0x3FE0EB524BAFC918 //ln(1/frcpa(1+ 178/256)
data8 0x3FE0FFB54213A476 //ln(1/frcpa(1+ 179/256)
data8 0x3FE114253DA97D9F //ln(1/frcpa(1+ 180/256)
data8 0x3FE128A24F1D9AFF //ln(1/frcpa(1+ 181/256)
data8 0x3FE1365252BF0865 //ln(1/frcpa(1+ 182/256)
data8 0x3FE14AE558B4A92D //ln(1/frcpa(1+ 183/256)
data8 0x3FE15F85A19C765B //ln(1/frcpa(1+ 184/256)
data8 0x3FE16D4D38C119FA //ln(1/frcpa(1+ 185/256)
data8 0x3FE18203C20DD133 //ln(1/frcpa(1+ 186/256)
data8 0x3FE196C7BC4B1F3B //ln(1/frcpa(1+ 187/256)
data8 0x3FE1A4A738B7A33C //ln(1/frcpa(1+ 188/256)
data8 0x3FE1B981C0C9653D //ln(1/frcpa(1+ 189/256)
data8 0x3FE1CE69E8BB106B //ln(1/frcpa(1+ 190/256)
data8 0x3FE1DC619DE06944 //ln(1/frcpa(1+ 191/256)
data8 0x3FE1F160A2AD0DA4 //ln(1/frcpa(1+ 192/256)
data8 0x3FE2066D7740737E //ln(1/frcpa(1+ 193/256)
data8 0x3FE2147DBA47A394 //ln(1/frcpa(1+ 194/256)
data8 0x3FE229A1BC5EBAC3 //ln(1/frcpa(1+ 195/256)
data8 0x3FE237C1841A502E //ln(1/frcpa(1+ 196/256)
data8 0x3FE24CFCE6F80D9A //ln(1/frcpa(1+ 197/256)
data8 0x3FE25B2C55CD5762 //ln(1/frcpa(1+ 198/256)
data8 0x3FE2707F4D5F7C41 //ln(1/frcpa(1+ 199/256)
data8 0x3FE285E0842CA384 //ln(1/frcpa(1+ 200/256)
data8 0x3FE294294708B773 //ln(1/frcpa(1+ 201/256)
data8 0x3FE2A9A2670AFF0C //ln(1/frcpa(1+ 202/256)
data8 0x3FE2B7FB2C8D1CC1 //ln(1/frcpa(1+ 203/256)
data8 0x3FE2C65A6395F5F5 //ln(1/frcpa(1+ 204/256)
data8 0x3FE2DBF557B0DF43 //ln(1/frcpa(1+ 205/256)
data8 0x3FE2EA64C3F97655 //ln(1/frcpa(1+ 206/256)
data8 0x3FE3001823684D73 //ln(1/frcpa(1+ 207/256)
data8 0x3FE30E97E9A8B5CD //ln(1/frcpa(1+ 208/256)
data8 0x3FE32463EBDD34EA //ln(1/frcpa(1+ 209/256)
data8 0x3FE332F4314AD796 //ln(1/frcpa(1+ 210/256)
data8 0x3FE348D90E7464D0 //ln(1/frcpa(1+ 211/256)
data8 0x3FE35779F8C43D6E //ln(1/frcpa(1+ 212/256)
data8 0x3FE36621961A6A99 //ln(1/frcpa(1+ 213/256)
data8 0x3FE37C299F3C366A //ln(1/frcpa(1+ 214/256)
data8 0x3FE38AE2171976E7 //ln(1/frcpa(1+ 215/256)
data8 0x3FE399A157A603E7 //ln(1/frcpa(1+ 216/256)
data8 0x3FE3AFCCFE77B9D1 //ln(1/frcpa(1+ 217/256)
data8 0x3FE3BE9D503533B5 //ln(1/frcpa(1+ 218/256)
data8 0x3FE3CD7480B4A8A3 //ln(1/frcpa(1+ 219/256)
data8 0x3FE3E3C43918F76C //ln(1/frcpa(1+ 220/256)
data8 0x3FE3F2ACB27ED6C7 //ln(1/frcpa(1+ 221/256)
data8 0x3FE4019C2125CA93 //ln(1/frcpa(1+ 222/256)
data8 0x3FE4181061389722 //ln(1/frcpa(1+ 223/256)
data8 0x3FE42711518DF545 //ln(1/frcpa(1+ 224/256)
data8 0x3FE436194E12B6BF //ln(1/frcpa(1+ 225/256)
data8 0x3FE445285D68EA69 //ln(1/frcpa(1+ 226/256)
data8 0x3FE45BCC464C893A //ln(1/frcpa(1+ 227/256)
data8 0x3FE46AED21F117FC //ln(1/frcpa(1+ 228/256)
data8 0x3FE47A1527E8A2D3 //ln(1/frcpa(1+ 229/256)
data8 0x3FE489445EFFFCCC //ln(1/frcpa(1+ 230/256)
data8 0x3FE4A018BCB69835 //ln(1/frcpa(1+ 231/256)
data8 0x3FE4AF5A0C9D65D7 //ln(1/frcpa(1+ 232/256)
data8 0x3FE4BEA2A5BDBE87 //ln(1/frcpa(1+ 233/256)
data8 0x3FE4CDF28F10AC46 //ln(1/frcpa(1+ 234/256)
data8 0x3FE4DD49CF994058 //ln(1/frcpa(1+ 235/256)
data8 0x3FE4ECA86E64A684 //ln(1/frcpa(1+ 236/256)
data8 0x3FE503C43CD8EB68 //ln(1/frcpa(1+ 237/256)
data8 0x3FE513356667FC57 //ln(1/frcpa(1+ 238/256)
data8 0x3FE522AE0738A3D8 //ln(1/frcpa(1+ 239/256)
data8 0x3FE5322E26867857 //ln(1/frcpa(1+ 240/256)
data8 0x3FE541B5CB979809 //ln(1/frcpa(1+ 241/256)
data8 0x3FE55144FDBCBD62 //ln(1/frcpa(1+ 242/256)
data8 0x3FE560DBC45153C7 //ln(1/frcpa(1+ 243/256)
data8 0x3FE5707A26BB8C66 //ln(1/frcpa(1+ 244/256)
data8 0x3FE587F60ED5B900 //ln(1/frcpa(1+ 245/256)
data8 0x3FE597A7977C8F31 //ln(1/frcpa(1+ 246/256)
data8 0x3FE5A760D634BB8B //ln(1/frcpa(1+ 247/256)
data8 0x3FE5B721D295F10F //ln(1/frcpa(1+ 248/256)
data8 0x3FE5C6EA94431EF9 //ln(1/frcpa(1+ 249/256)
data8 0x3FE5D6BB22EA86F6 //ln(1/frcpa(1+ 250/256)
data8 0x3FE5E6938645D390 //ln(1/frcpa(1+ 251/256)
data8 0x3FE5F673C61A2ED2 //ln(1/frcpa(1+ 252/256)
data8 0x3FE6065BEA385926 //ln(1/frcpa(1+ 253/256)
data8 0x3FE6164BFA7CC06B //ln(1/frcpa(1+ 254/256)
data8 0x3FE62643FECF9743 //ln(1/frcpa(1+ 255/256)
//
// [2;4)
data8 0xBEB2CC7A38B9355F,0x3F035F2D1833BF4C // A10,A9
data8 0xBFF51BAA7FD27785,0x3FFC9D5D5B6CDEFF // A2,A1
data8 0xBF421676F9CB46C7,0x3F7437F2FA1436C6 // A8,A7
data8 0xBFD7A7041DE592FE,0x3FE9F107FEE8BD29 // A4,A3
// [4;8)
data8 0x3F6BBBD68451C0CD,0xBF966EC3272A16F7 // A10,A9
data8 0x40022A24A39AD769,0x4014190EDF49C8C5 // A2,A1
data8 0x3FB130FD016EE241,0xBFC151B46E635248 // A8,A7
data8 0x3FDE8F611965B5FE,0xBFEB5110EB265E3D // A4,A3
// [8;16)
data8 0x3F736EF93508626A,0xBF9FE5DBADF58AF1 // A10,A9
data8 0x40110A9FC5192058,0x40302008A6F96B29 // A2,A1
data8 0x3FB8E74E0CE1E4B5,0xBFC9B5DA78873656 // A8,A7
data8 0x3FE99D0DF10022DC,0xBFF829C0388F9484 // A4,A3
// [16;32)
data8 0x3F7FFF9D6D7E9269,0xBFAA780A249AEDB1 // A10,A9
data8 0x402082A807AEA080,0x4045ED9868408013 // A2,A1
data8 0x3FC4E1E54C2F99B7,0xBFD5DE2D6FFF1490 // A8,A7
data8 0x3FF75FC89584AE87,0xC006B4BADD886CAE // A4,A3
// [32;64)
data8 0x3F8CE54375841A5F,0xBFB801ABCFFA1BE2 // A10,A9
data8 0x403040A8B1815BDA,0x405B99A917D24B7A // A2,A1
data8 0x3FD30CAB81BFFA03,0xBFE41AEF61ECF48B // A8,A7
data8 0x400650CC136BEC43,0xC016022046E8292B // A4,A3
// [64;128)
data8 0x3F9B69BD22CAA8B8,0xBFC6D48875B7A213 // A10,A9
data8 0x40402028CCAA2F6D,0x40709AACEB3CBE0F // A2,A1
data8 0x3FE22C6A5924761E,0xBFF342F5F224523D // A8,A7
data8 0x4015CD405CCA331F,0xC025AAD10482C769 // A4,A3
// [128;256)
data8 0x3FAAAD9CD0E40D06,0xBFD63FC8505D80CB // A10,A9
data8 0x40501008D56C2648,0x408364794B0F4376 // A2,A1
data8 0x3FF1BE0126E00284,0xC002D8E3F6F7F7CA // A8,A7
data8 0x40258C757E95D860,0xC0357FA8FD398011 // A4,A3
// [256;512)
data8 0x3FBA4DAC59D49FEB,0xBFE5F476D1C43A77 // A10,A9
data8 0x40600800D890C7C6,0x40962C42AAEC8EF0 // A2,A1
data8 0x40018680ECF19B89,0xC012A3EB96FB7BA4 // A8,A7
data8 0x40356C4CDD3B60F9,0xC0456A34BF18F440 // A4,A3
// [512;1024)
data8 0x3FCA1B54F6225A5A,0xBFF5CD67BA10E048 // A10,A9
data8 0x407003FED94C58C2,0x40A8F30B4ACBCD22 // A2,A1
data8 0x40116A135EB66D8C,0xC022891B1CED527E // A8,A7
data8 0x40455C4617FDD8BC,0xC0555F82729E59C4 // A4,A3
// [1024;2048)
data8 0x3FD9FFF9095C6EC9,0xC005B88CB25D76C9 // A10,A9
data8 0x408001FE58FA734D,0x40BBB953BAABB0F3 // A2,A1
data8 0x40215B2F9FEB5D87,0xC0327B539DEA5058 // A8,A7
data8 0x40555444B3E8D64D,0xC0655A2B26F9FC8A // A4,A3
// [2048;4096)
data8 0x3FE9F065A1C3D6B1,0xC015ACF6FAE8D78D // A10,A9
data8 0x409000FE383DD2B7,0x40CE7F5C1E8BCB8B // A2,A1
data8 0x40315324E5DB2EBE,0xC04274194EF70D18 // A8,A7
data8 0x4065504353FF2207,0xC075577FE1BFE7B6 // A4,A3
// [4096;8192)
data8 0x3FF9E6FBC6B1C70D,0xC025A62DAF76F85D // A10,A9
data8 0x40A0007E2F61EBE8,0x40E0A2A23FB5F6C3 // A2,A1
data8 0x40414E9BC0A0141A,0xC0527030F2B69D43 // A8,A7
data8 0x40754E417717B45B,0xC085562A447258E5 // A4,A3
//
data8 0xbfdffffffffaea15 // P1
data8 0x3FDD8B618D5AF8FE // point of local minimum on [1;2]
data8 0x3FED67F1C864BEB5 // ln(sqrt(2*Pi))
data8 0x4008000000000000 // 3.0
//
data8 0xBF9E1C289FB224AB,0x3FBF7422445C9460 // A6,A5
data8 0xBFF01E76D66F8D8A // A0
data8 0xBFE2788CFC6F91DA // A1 [1.0;1.25)
data8 0x3FCB8CC69000EB5C,0xBFD41997A0C2C641 // A6,A5
data8 0x3FFCAB0BFA0EA462 // A0
data8 0xBFBF19B9BCC38A42 // A0 [1.25;1.5)
data8 0x3FD51EE4DE0A364C,0xBFE00D7F98A16E4B // A6,A5
data8 0x40210CE1F327E9E4 // A0
data8 0x4001DB08F9DFA0CC // A0 [1.5;1.75)
data8 0x3FE24F606742D252,0xBFEC81D7D12574EC // A6,A5
data8 0x403BE636A63A9C27 // A0
data8 0x4000A0CB38D6CF0A // A0 [1.75;2.0)
data8 0x3FF1029A9DD542B4,0xBFFAD37C209D3B25 // A6,A5
data8 0x405385E6FD9BE7EA // A0
data8 0x478895F1C0000000 // Overflow boundary
data8 0x400062D97D26B523,0xC00A03E1529FF023 // A6,A5
data8 0x4069204C51E566CE // A0
data8 0x0000000000000000 // pad
data8 0x40101476B38FD501,0xC0199DE7B387C0FC // A6,A5
data8 0x407EB8DAEC83D759 // A0
data8 0x0000000000000000 // pad
data8 0x401FDB008D65125A,0xC0296B506E665581 // A6,A5
data8 0x409226D93107EF66 // A0
data8 0x0000000000000000 // pad
data8 0x402FB3EAAF3E7B2D,0xC039521142AD8E0D // A6,A5
data8 0x40A4EFA4F072792E // A0
data8 0x0000000000000000 // pad
data8 0x403FA024C66B2563,0xC0494569F250E691 // A6,A5
data8 0x40B7B747C9235BB8 // A0
data8 0x0000000000000000 // pad
data8 0x404F9607D6DA512C,0xC0593F0B2EDDB4BC // A6,A5
data8 0x40CA7E29C5F16DE2 // A0
data8 0x0000000000000000 // pad
data8 0x405F90C5F613D98D,0xC0693BD130E50AAF // A6,A5
data8 0x40DD4495238B190C // A0
data8 0x0000000000000000 // pad
//
// polynomial approximation of ln(sin(Pi*x)/(Pi*x)), |x| <= 0.5
data8 0xBFD58731A486E820,0xBFA4452CC28E15A9 // S16,S14
data8 0xBFD013F6E1B86C4F,0xBFD5B3F19F7A341F // S8,S6
data8 0xBFC86A0D5252E778,0xBFC93E08C9EE284B // S12,S10
data8 0xBFE15132555C9EDD,0xBFFA51A662480E35 // S4,S2
//
// [1.0;1.25)
data8 0xBFA697D6775F48EA,0x3FB9894B682A98E7 // A9,A8
data8 0xBFCA8969253CFF55,0x3FD15124EFB35D9D // A5,A4
data8 0xBFC1B00158AB719D,0x3FC5997D04E7F1C1 // A7,A6
data8 0xBFD9A4D50BAFF989,0x3FEA51A661F5176A // A3,A2
// [1.25;1.5)
data8 0x3F838E0D35A6171A,0xBF831BBBD61313B7 // A8,A7
data8 0x3FB08B40196425D0,0xBFC2E427A53EB830 // A4,A3
data8 0x3F9285DDDC20D6C3,0xBFA0C90C9C223044 // A6,A5
data8 0x3FDEF72BC8F5287C,0x3D890B3DAEBC1DFC // A2,A1
// [1.5;1.75)
data8 0x3F65D5A7EB31047F,0xBFA44EAC9BFA7FDE // A8,A7
data8 0x40051FEFE7A663D8,0xC012A5CFE00A2522 // A4,A3
data8 0x3FD0E1583AB00E08,0xBFF084AF95883BA5 // A6,A5
data8 0x40185982877AE0A2,0xC015F83DB73B57B7 // A2,A1
// [1.75;2.0)
data8 0x3F4A9222032EB39A,0xBF8CBC9587EEA5A3 // A8,A7
data8 0x3FF795400783BE49,0xC00851BC418B8A25 // A4,A3
data8 0x3FBBC992783E8C5B,0xBFDFA67E65E89B29 // A6,A5
data8 0x4012B408F02FAF88,0xC013284CE7CB0C39 // A2,A1
//
// roots
data8 0xC003A7FC9600F86C // -2.4570247382208005860
data8 0xC009260DBC9E59AF // -3.1435808883499798405
data8 0xC005FB410A1BD901 // -2.7476826467274126919
data8 0xC00FA471547C2FE5 // -3.9552942848585979085
//
// polynomial approximation of ln(GAMMA(x)) near roots
// near -2.4570247382208005860
data8 0x3FF694A6058D9592,0x40136EEBB003A92B // R3,R2
data8 0x3FF83FE966AF5360,0x3C90323B6D1FE86D // R1,R0
// near -3.1435808883499798405
data8 0x405C11371268DA38,0x4039D4D2977D2C23 // R3,R2
data8 0x401F20A65F2FAC62,0x3CDE9605E3AE7A62 // R1,R0
// near -2.7476826467274126919
data8 0xC034185AC31314FF,0x4023267F3C28DFE3 // R3,R2
data8 0xBFFEA12DA904B194,0x3CA8FB8530BA7689 // R1,R0
// near -2.7476826467274126919
data8 0xC0AD25359E70C888,0x406F76DEAEA1B8C6 // R3,R2
data8 0xC034B99D966C5644,0xBCBDDC0336980B58 // R1,R0
LOCAL_OBJECT_END(lgammaf_data)
//*********************************************************************
.section .text
GLOBAL_LIBM_ENTRY(__libm_lgammaf)
{ .mfi
getf.exp GR_SignExp = f8
frcpa.s1 FR_InvX,p0 = f1,f8
mov GR_ExpOf2 = 0x10000
}
{ .mfi
addl GR_ad_Data = @ltoff(lgammaf_data),gp
fcvt.fx.s1 FR_int_N = f8
mov GR_ExpMask = 0x1ffff
};;
{ .mfi
getf.sig GR_Sig = f8
fclass.m p13,p0 = f8,0x1EF // is x NaTVal, NaN,
// +/-0, +/-INF or +/-deno?
mov GR_ExpBias = 0xffff
}
{ .mfi
ld8 GR_ad_Data = [GR_ad_Data]
fma.s1 FR_Xp1 = f8,f1,f1
mov GR_StirlBound = 0x1000C
};;
{ .mfi
setf.exp FR_2 = GR_ExpOf2
fmerge.se FR_x = f1,f8
dep.z GR_Ind = GR_SignExp,3,4
}
{ .mfi
cmp.eq p8,p0 = GR_SignExp,GR_ExpBias
fcvt.fx.trunc.s1 FR_int_Ntrunc = f8
and GR_Exp = GR_ExpMask,GR_SignExp
};;
{ .mfi
add GR_ad_C650 = 0xB20,GR_ad_Data
fcmp.lt.s1 p14,p15 = f8,f0
extr.u GR_Ind4T = GR_Sig,55,8
}
{ .mfb
sub GR_PureExp = GR_Exp,GR_ExpBias
fnorm.s1 FR_NormX = f8
// jump if x is NaTVal, NaN, +/-0, +/-INF or +/-deno
(p13) br.cond.spnt lgammaf_spec
};;
lgammaf_core:
{ .mfi
ldfpd FR_P1,FR_LocalMin = [GR_ad_C650],16
fms.s1 FR_xm2 = f8,f1,f1
add GR_ad_Co = 0x820,GR_ad_Data
}
{ .mib
ldfpd FR_P3,FR_P2 = [GR_ad_Data],16
cmp.ltu p9,p0 = GR_SignExp,GR_ExpBias
// jump if x is from the interval [1; 2)
(p8) br.cond.spnt lgammaf_1_2
};;
{ .mfi
setf.sig FR_int_Ln = GR_PureExp
fms.s1 FR_r = FR_InvX,f8,f1
shladd GR_ad_Co = GR_Ind,3,GR_ad_Co
}
{ .mib
ldfpd FR_LnSqrt2Pi,FR_3 = [GR_ad_C650],16
cmp.lt p13,p12 = GR_Exp,GR_StirlBound
// jump if x is from the interval (0; 1)
(p9) br.cond.spnt lgammaf_0_1
};;
{ .mfi
ldfpd FR_Ln2,FR_05 = [GR_ad_Data],16
fma.s1 FR_Xp2 = f1,f1,FR_Xp1 // (x+2)
shladd GR_ad_C650 = GR_Ind,2,GR_ad_C650
}
{ .mfi
add GR_ad_Ce = 0x20,GR_ad_Co
nop.f 0
add GR_ad_C43 = 0x30,GR_ad_Co
};;
{ .mfi
// load coefficients of polynomial approximation
// of ln(GAMMA(x)), 2 <= x < 2^13
(p13) ldfpd FR_A10,FR_A9 = [GR_ad_Co],16
fcvt.xf FR_N = FR_int_N
cmp.eq.unc p6,p7 = GR_ExpOf2,GR_SignExp
}
{ .mib
(p13) ldfpd FR_A8,FR_A7 = [GR_ad_Ce]
(p14) cmp.le.unc p9,p0 = GR_StirlBound,GR_Exp
// jump if x is less or equal to -2^13
(p9) br.cond.spnt lgammaf_negstirling
};;
.pred.rel "mutex",p6,p7
{ .mfi
(p13) ldfpd FR_A6,FR_A5 = [GR_ad_C650],16
(p6) fma.s1 FR_x = f0,f0,FR_NormX
shladd GR_ad_T = GR_Ind4T,3,GR_ad_Data
}
{ .mfi
(p13) ldfpd FR_A4,FR_A3 = [GR_ad_C43]
(p7) fms.s1 FR_x = FR_x,f1,f1
(p14) mov GR_ReqBound = 0x20005
};;
{ .mfi
(p13) ldfpd FR_A2,FR_A1 = [GR_ad_Co],16
fms.s1 FR_xm2 = FR_xm2,f1,f1
(p14) extr.u GR_Arg = GR_Sig,60,4
}
{ .mfi
mov GR_SignOfGamma = 1 // set sign of gamma(x) to 1
fcvt.xf FR_Ntrunc = FR_int_Ntrunc
nop.i 0
};;
{ .mfi
ldfd FR_T = [GR_ad_T]
fma.s1 FR_r2 = FR_r,FR_r,f0
shl GR_ReqBound = GR_ReqBound,3
}
{ .mfi
add GR_ad_Co = 0xCA0,GR_ad_Data
fnma.s1 FR_Req = FR_Xp1,FR_NormX,f0 // -x*(x+1)
(p14) shladd GR_Arg = GR_Exp,4,GR_Arg
};;
{ .mfi
(p13) ldfd FR_A0 = [GR_ad_C650]
fma.s1 FR_Xp3 = FR_2,f1,FR_Xp1 // (x+3)
(p14) cmp.le.unc p9,p0 = GR_Arg,GR_ReqBound
}
{ .mfi
(p14) add GR_ad_Ce = 0x20,GR_ad_Co
fma.s1 FR_Xp4 = FR_2,FR_2,FR_NormX // (x+4)
(p15) add GR_ad_OvfBound = 0xBB8,GR_ad_Data
};;
{ .mfi
// load coefficients of polynomial approximation
// of ln(sin(Pi*xf)/(Pi*xf)), |xf| <= 0.5
(p14) ldfpd FR_S16,FR_S14 = [GR_ad_Co],16
(p14) fms.s1 FR_Xf = FR_NormX,f1,FR_N // xf = x - [x]
(p14) sub GR_SignOfGamma = r0,GR_SignOfGamma // set sign of
// gamma(x) to -1
}
{ .mfb
(p14) ldfpd FR_S12,FR_S10 = [GR_ad_Ce],16
fma.s1 FR_Xp5 = FR_2,FR_2,FR_Xp1 // (x+5)
// jump if x is from the interval (-9; 0)
(p9) br.cond.spnt lgammaf_negrecursion
};;
{ .mfi
(p14) ldfpd FR_S8,FR_S6 = [GR_ad_Co],16
fma.s1 FR_P32 = FR_P3,FR_r,FR_P2
nop.i 0
}
{ .mfb
(p14) ldfpd FR_S4,FR_S2 = [GR_ad_Ce],16
fma.s1 FR_x2 = FR_x,FR_x,f0
// jump if x is from the interval (-2^13; -9)
(p14) br.cond.spnt lgammaf_negpoly
};;
{ .mfi
ldfd FR_OverflowBound = [GR_ad_OvfBound]
(p12) fcvt.xf FR_N = FR_int_Ln
// set p9 if signgum is 32-bit int
// set p10 if signgum is 64-bit int
cmp.eq p10,p9 = 8,r34
}
{ .mfi
nop.m 0
(p12) fma.s1 FR_P10 = FR_P1,FR_r,f1
nop.i 0
};;
.pred.rel "mutex",p6,p7
.pred.rel "mutex",p9,p10
{ .mfi
// store sign of gamma(x) as 32-bit int
(p9) st4 [r33] = GR_SignOfGamma
(p6) fma.s1 FR_xx = FR_x,FR_xm2,f0
nop.i 0
}
{ .mfi
// store sign of gamma(x) as 64-bit int
(p10) st8 [r33] = GR_SignOfGamma
(p7) fma.s1 FR_xx = f0,f0,FR_x
nop.i 0
};;
{ .mfi
nop.m 0
(p13) fma.s1 FR_A9 = FR_A10,FR_x,FR_A9
nop.i 0
}
{ .mfi
nop.m 0
(p13) fma.s1 FR_A7 = FR_A8,FR_x,FR_A7
nop.i 0
};;
{ .mfi
nop.m 0
(p13) fma.s1 FR_A5 = FR_A6,FR_x,FR_A5
nop.i 0
}
{ .mfi
nop.m 0
(p13) fma.s1 FR_A3 = FR_A4,FR_x,FR_A3
nop.i 0
};;
{ .mfi
nop.m 0
(p15) fcmp.eq.unc.s1 p8,p0 = FR_NormX,FR_2 // is input argument 2.0?
nop.i 0
}
{ .mfi
nop.m 0
(p13) fma.s1 FR_A1 = FR_A2,FR_x,FR_A1
nop.i 0
};;
{ .mfi
nop.m 0
(p12) fma.s1 FR_T = FR_N,FR_Ln2,FR_T
nop.i 0
}
{ .mfi
nop.m 0
(p12) fma.s1 FR_P32 = FR_P32,FR_r2,FR_P10
nop.i 0
};;
{ .mfi
nop.m 0
(p13) fma.s1 FR_x4 = FR_x2,FR_x2,f0
nop.i 0
}
{ .mfi
nop.m 0
(p13) fma.s1 FR_x3 = FR_x2,FR_xx,f0
nop.i 0
};;
{ .mfi
nop.m 0
(p13) fma.s1 FR_A7 = FR_A9,FR_x2,FR_A7
nop.i 0
}
{ .mfb
nop.m 0
(p8) fma.s.s0 f8 = f0,f0,f0
(p8) br.ret.spnt b0 // fast exit for 2.0
};;
{ .mfi
nop.m 0
(p6) fma.s1 FR_A0 = FR_A0,FR_xm2,f0
nop.i 0
}
{ .mfi
nop.m 0
(p13) fma.s1 FR_A3 = FR_A5,FR_x2,FR_A3
nop.i 0
};;
{ .mfi
nop.m 0
(p15) fcmp.le.unc.s1 p8,p0 = FR_OverflowBound,FR_NormX // overflow test
nop.i 0
}
{ .mfi
nop.m 0
(p12) fms.s1 FR_xm05 = FR_NormX,f1,FR_05
nop.i 0
};;
{ .mfi
nop.m 0
(p12) fma.s1 FR_Ln = FR_P32,FR_r,FR_T
nop.i 0
}
{ .mfi
nop.m 0
(p12) fms.s1 FR_LnSqrt2Pi = FR_LnSqrt2Pi,f1,FR_NormX
nop.i 0
};;
{ .mfi
nop.m 0
(p13) fma.s1 FR_A0 = FR_A1,FR_xx,FR_A0
nop.i 0
}
{ .mfb
nop.m 0
(p13) fma.s1 FR_A3 = FR_A7,FR_x4,FR_A3
// jump if result overflows
(p8) br.cond.spnt lgammaf_overflow
};;
.pred.rel "mutex",p12,p13
{ .mfi
nop.m 0
(p12) fma.s.s0 f8 = FR_Ln,FR_xm05,FR_LnSqrt2Pi
nop.i 0
}
{ .mfb
nop.m 0
(p13) fma.s.s0 f8 = FR_A3,FR_x3,FR_A0
br.ret.sptk b0
};;
// branch for calculating of ln(GAMMA(x)) for 0 < x < 1
//---------------------------------------------------------------------
.align 32
lgammaf_0_1:
{ .mfi
getf.sig GR_Ind = FR_Xp1
fma.s1 FR_r2 = FR_r,FR_r,f0
mov GR_fff7 = 0xFFF7
}
{ .mfi
ldfpd FR_Ln2,FR_05 = [GR_ad_Data],16
fma.s1 FR_P32 = FR_P3,FR_r,FR_P2
// input argument can't be equal to 1.0
cmp.eq p0,p14 = r0,r0
};;
{ .mfi
getf.exp GR_Exp = FR_w
fcvt.xf FR_N = FR_int_Ln
add GR_ad_Co = 0xCE0,GR_ad_Data
}
{ .mfi
shladd GR_ad_T = GR_Ind4T,3,GR_ad_Data
fma.s1 FR_P10 = FR_P1,FR_r,f1
add GR_ad_Ce = 0xD00,GR_ad_Data
};;
{ .mfi
ldfd FR_T = [GR_ad_T]
fma.s1 FR_w2 = FR_w,FR_w,f0
extr.u GR_Ind = GR_Ind,61,2
}
{ .mfi
nop.m 0
fma.s1 FR_Q32 = FR_P3,FR_w,FR_P2
//// add GR_ad_C0 = 0xB30,GR_ad_Data
add GR_ad_C0 = 0xB38,GR_ad_Data
};;
{ .mfi
and GR_Exp = GR_Exp,GR_ExpMask
nop.f 0
shladd GR_IndX8 = GR_Ind,3,r0
}
{ .mfi
shladd GR_IndX2 = GR_Ind,1,r0
fma.s1 FR_Q10 = FR_P1,FR_w,f1
cmp.eq p6,p15 = 0,GR_Ind
};;
{ .mfi
shladd GR_ad_Co = GR_IndX8,3,GR_ad_Co
(p6) fma.s1 FR_x = f0,f0,FR_NormX
shladd GR_ad_C0 = GR_IndX2,4,GR_ad_C0
}
{ .mfi
shladd GR_ad_Ce = GR_IndX8,3,GR_ad_Ce
nop.f 0
(p15) cmp.eq.unc p7,p8 = 1,GR_Ind
};;
.pred.rel "mutex",p7,p8
{ .mfi
ldfpd FR_A8,FR_A7 = [GR_ad_Co],16
(p7) fms.s1 FR_x = FR_NormX,f1,FR_LocalMin
cmp.ge p10,p11 = GR_Exp,GR_fff7
}
{ .mfb
ldfpd FR_A6,FR_A5 = [GR_ad_Ce],16
(p8) fma.s1 FR_x = f1,f1,FR_NormX
br.cond.sptk lgamma_0_2_core
};;
// branch for calculating of ln(GAMMA(x)) for 1 <= x < 2
//---------------------------------------------------------------------
.align 32
lgammaf_1_2:
{ .mfi
add GR_ad_Co = 0xCF0,GR_ad_Data
fcmp.eq.s1 p14,p0 = f1,FR_NormX // is input argument 1.0?
extr.u GR_Ind = GR_Sig,61,2
}
{ .mfi
add GR_ad_Ce = 0xD10,GR_ad_Data
nop.f 0
//// add GR_ad_C0 = 0xB40,GR_ad_Data
add GR_ad_C0 = 0xB48,GR_ad_Data
};;
{ .mfi
shladd GR_IndX8 = GR_Ind,3,r0
nop.f 0
shladd GR_IndX2 = GR_Ind,1,r0
}
{ .mfi
cmp.eq p6,p15 = 0,GR_Ind // p6 <- x from [1;1.25)
nop.f 0
cmp.ne p9,p0 = r0,r0
};;
{ .mfi
shladd GR_ad_Co = GR_IndX8,3,GR_ad_Co
(p6) fms.s1 FR_x = FR_NormX,f1,f1 // reduced x for [1;1.25)
shladd GR_ad_C0 = GR_IndX2,4,GR_ad_C0
}
{ .mfi
shladd GR_ad_Ce = GR_IndX8,3,GR_ad_Ce
(p14) fma.s.s0 f8 = f0,f0,f0
(p15) cmp.eq.unc p7,p8 = 1,GR_Ind // p7 <- x from [1.25;1.5)
};;
.pred.rel "mutex",p7,p8
{ .mfi
ldfpd FR_A8,FR_A7 = [GR_ad_Co],16
(p7) fms.s1 FR_x = FR_xm2,f1,FR_LocalMin
nop.i 0
}
{ .mfi
ldfpd FR_A6,FR_A5 = [GR_ad_Ce],16
(p8) fma.s1 FR_x = f0,f0,FR_NormX
(p9) cmp.eq.unc p10,p11 = r0,r0
};;
lgamma_0_2_core:
{ .mmi
ldfpd FR_A4,FR_A3 = [GR_ad_Co],16
ldfpd FR_A2,FR_A1 = [GR_ad_Ce],16
mov GR_SignOfGamma = 1 // set sign of gamma(x) to 1
};;
{ .mfi
// add GR_ad_C0 = 8,GR_ad_C0
ldfd FR_A0 = [GR_ad_C0]
nop.f 0
// set p13 if signgum is 32-bit int
// set p15 if signgum is 64-bit int
cmp.eq p15,p13 = 8,r34
};;
.pred.rel "mutex",p13,p15
{ .mmf
// store sign of gamma(x)
(p13) st4 [r33] = GR_SignOfGamma // as 32-bit int
(p15) st8 [r33] = GR_SignOfGamma // as 64-bit int
(p11) fma.s1 FR_Q32 = FR_Q32,FR_w2,FR_Q10
};;
{ .mfb
nop.m 0
(p10) fma.s1 FR_P32 = FR_P32,FR_r2,FR_P10
(p14) br.ret.spnt b0 // fast exit for 1.0
};;
{ .mfi
nop.m 0
(p10) fma.s1 FR_T = FR_N,FR_Ln2,FR_T
cmp.eq p6,p7 = 0,GR_Ind // p6 <- x from [1;1.25)
}
{ .mfi
nop.m 0
fma.s1 FR_x2 = FR_x,FR_x,f0
cmp.eq p8,p0 = r0,r0 // set p8 to 1 that means we on [1;2]
};;
{ .mfi
nop.m 0
(p11) fma.s1 FR_Ln = FR_Q32,FR_w,f0
nop.i 0
}
{ .mfi
nop.m 0
nop.f 0
nop.i 0
};;
.pred.rel "mutex",p6,p7
{ .mfi
nop.m 0
(p6) fma.s1 FR_xx = f0,f0,FR_x
nop.i 0
}
{ .mfi
nop.m 0
(p7) fma.s1 FR_xx = f0,f0,f1
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_A7 = FR_A8,FR_x,FR_A7
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_A5 = FR_A6,FR_x,FR_A5
(p9) cmp.ne p8,p0 = r0,r0 // set p8 to 0 that means we on [0;1]
};;
{ .mfi
nop.m 0
fma.s1 FR_A3 = FR_A4,FR_x,FR_A3
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_A1 = FR_A2,FR_x,FR_A1
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_x4 = FR_x2,FR_x2,f0
nop.i 0
}
{ .mfi
nop.m 0
(p10) fma.s1 FR_Ln = FR_P32,FR_r,FR_T
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_A5 = FR_A7,FR_x2,FR_A5
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_A1 = FR_A3,FR_x2,FR_A1
nop.i 0
};;
.pred.rel "mutex",p9,p8
{ .mfi
nop.m 0
(p9) fms.d.s1 FR_A0 = FR_A0,FR_xx,FR_Ln
nop.i 0
}
{ .mfi
nop.m 0
(p8) fms.s1 FR_A0 = FR_A0,FR_xx,f0
nop.i 0
};;
{ .mfi
nop.m 0
fma.d.s1 FR_A1 = FR_A5,FR_x4,FR_A1
nop.i 0
}
{ .mfi
nop.m 0
nop.f 0
nop.i 0
};;
.pred.rel "mutex",p6,p7
{ .mfi
nop.m 0
(p6) fma.s.s0 f8 = FR_A1,FR_x2,FR_A0
nop.i 0
}
{ .mfb
nop.m 0
(p7) fma.s.s0 f8 = FR_A1,FR_x,FR_A0
br.ret.sptk b0
};;
// branch for calculating of ln(GAMMA(x)) for -9 < x < 1
//---------------------------------------------------------------------
.align 32
lgammaf_negrecursion:
{ .mfi
getf.sig GR_N = FR_int_Ntrunc
fms.s1 FR_1pXf = FR_Xp2,f1,FR_Ntrunc // 1 + (x+1) - [x]
mov GR_Neg2 = 2
}
{ .mfi
add GR_ad_Co = 0xCE0,GR_ad_Data
fms.s1 FR_Xf = FR_Xp1,f1,FR_Ntrunc // (x+1) - [x]
mov GR_Neg4 = 4
};;
{ .mfi
add GR_ad_Ce = 0xD00,GR_ad_Data
fma.s1 FR_Xp6 = FR_2,FR_2,FR_Xp2 // (x+6)
add GR_ad_C0 = 0xB30,GR_ad_Data
}
{ .mfi
sub GR_Neg2 = r0,GR_Neg2
fma.s1 FR_Xp7 = FR_2,FR_3,FR_Xp1 // (x+7)
sub GR_Neg4 = r0,GR_Neg4
};;
{ .mfi
cmp.ne p8,p0 = r0,GR_N
fcmp.eq.s1 p13,p0 = FR_NormX,FR_Ntrunc
and GR_IntNum = 0xF,GR_N
}
{ .mfi
cmp.lt p6,p0 = GR_N,GR_Neg2
fma.s1 FR_Xp8 = FR_2,FR_3,FR_Xp2 // (x+8)
cmp.lt p7,p0 = GR_N,GR_Neg4
};;
{ .mfi
getf.d GR_Arg = FR_NormX
(p6) fma.s1 FR_Xp2 = FR_Xp2,FR_Xp3,f0
(p8) tbit.z.unc p14,p15 = GR_IntNum,0
}
{ .mfi
sub GR_RootInd = 0xE,GR_IntNum
(p7) fma.s1 FR_Xp4 = FR_Xp4,FR_Xp5,f0
add GR_ad_Root = 0xDE0,GR_ad_Data
};;
{ .mfi
shladd GR_ad_Root = GR_RootInd,3,GR_ad_Root
fms.s1 FR_x = FR_Xp1,f1,FR_Ntrunc // (x+1) - [x]
nop.i 0
}
{ .mfb
nop.m 0
nop.f 0
(p13) br.cond.spnt lgammaf_singularity
};;
.pred.rel "mutex",p14,p15
{ .mfi
cmp.gt p6,p0 = 0xA,GR_IntNum
(p14) fma.s1 FR_Req = FR_Req,FR_Xf,f0
cmp.gt p7,p0 = 0xD,GR_IntNum
}
{ .mfi
(p15) mov GR_SignOfGamma = 1 // set sign of gamma(x) to 1
(p15) fnma.s1 FR_Req = FR_Req,FR_Xf,f0
cmp.leu p0,p13 = 2,GR_RootInd
};;
{ .mfi
nop.m 0
(p6) fma.s1 FR_Xp6 = FR_Xp6,FR_Xp7,f0
(p13) add GR_ad_RootCo = 0xE00,GR_ad_Data
};;
{ .mfi
nop.m 0
fcmp.eq.s1 p12,p11 = FR_1pXf,FR_2
nop.i 0
};;
{ .mfi
getf.sig GR_Sig = FR_1pXf
fcmp.le.s1 p9,p0 = FR_05,FR_Xf
nop.i 0
}
{ .mfi
(p13) shladd GR_RootInd = GR_RootInd,4,r0
(p7) fma.s1 FR_Xp2 = FR_Xp2,FR_Xp4,f0
(p8) cmp.gt.unc p10,p0 = 0x9,GR_IntNum
};;
.pred.rel "mutex",p11,p12
{ .mfi
nop.m 0
(p10) fma.s1 FR_Req = FR_Req,FR_Xp8,f0
(p11) extr.u GR_Ind = GR_Sig,61,2
}
{ .mfi
(p13) add GR_RootInd = GR_RootInd,GR_RootInd
nop.f 0
(p12) mov GR_Ind = 3
};;
{ .mfi
shladd GR_IndX2 = GR_Ind,1,r0
nop.f 0
cmp.gt p14,p0 = 2,GR_Ind
}
{ .mfi
shladd GR_IndX8 = GR_Ind,3,r0
nop.f 0
cmp.eq p6,p0 = 1,GR_Ind
};;
.pred.rel "mutex",p6,p9
{ .mfi
shladd GR_ad_Co = GR_IndX8,3,GR_ad_Co
(p6) fms.s1 FR_x = FR_Xf,f1,FR_LocalMin
cmp.gt p10,p0 = 0xB,GR_IntNum
}
{ .mfi
shladd GR_ad_Ce = GR_IndX8,3,GR_ad_Ce
(p9) fma.s1 FR_x = f0,f0,FR_1pXf
shladd GR_ad_C0 = GR_IndX2,4,GR_ad_C0
};;
{ .mfi
// load coefficients of polynomial approximation
// of ln(GAMMA(x)), 1 <= x < 2
ldfpd FR_A8,FR_A7 = [GR_ad_Co],16
(p10) fma.s1 FR_Xp2 = FR_Xp2,FR_Xp6,f0
add GR_ad_C0 = 8,GR_ad_C0
}
{ .mfi
ldfpd FR_A6,FR_A5 = [GR_ad_Ce],16
nop.f 0
(p14) add GR_ad_Root = 0x10,GR_ad_Root
};;
{ .mfi
ldfpd FR_A4,FR_A3 = [GR_ad_Co],16
nop.f 0
add GR_ad_RootCe = 0xE10,GR_ad_Data
}
{ .mfi
ldfpd FR_A2,FR_A1 = [GR_ad_Ce],16
nop.f 0
(p14) add GR_RootInd = 0x40,GR_RootInd
};;
{ .mmi
ldfd FR_A0 = [GR_ad_C0]
(p13) add GR_ad_RootCo = GR_ad_RootCo,GR_RootInd
(p13) add GR_ad_RootCe = GR_ad_RootCe,GR_RootInd
};;
{ .mmi
(p13) ld8 GR_Root = [GR_ad_Root]
(p13) ldfd FR_Root = [GR_ad_Root]
mov GR_ExpBias = 0xffff
};;
{ .mfi
nop.m 0
fma.s1 FR_x2 = FR_x,FR_x,f0
nop.i 0
}
{ .mlx
(p8) cmp.gt.unc p10,p0 = 0xF,GR_IntNum
movl GR_Dx = 0x000000014F8B588E
};;
{ .mfi
// load coefficients of polynomial approximation
// of ln(GAMMA(x)), x is close to one of negative roots
(p13) ldfpd FR_R3,FR_R2 = [GR_ad_RootCo]
// arguments for logarithm
(p10) fma.s1 FR_Req = FR_Req,FR_Xp2,f0
mov GR_ExpMask = 0x1ffff
}
{ .mfi
(p13) ldfpd FR_R1,FR_R0 = [GR_ad_RootCe]
nop.f 0
// set p9 if signgum is 32-bit int
// set p8 if signgum is 64-bit int
cmp.eq p8,p9 = 8,r34
};;
.pred.rel "mutex",p9,p8
{ .mfi
(p9) st4 [r33] = GR_SignOfGamma // as 32-bit int
fma.s1 FR_A7 = FR_A8,FR_x,FR_A7
(p13) sub GR_Root = GR_Arg,GR_Root
}
{ .mfi
(p8) st8 [r33] = GR_SignOfGamma // as 64-bit int
fma.s1 FR_A5 = FR_A6,FR_x,FR_A5
nop.i 0
};;
{ .mfi
nop.m 0
fms.s1 FR_w = FR_Req,f1,f1
(p13) add GR_Root = GR_Root,GR_Dx
}
{ .mfi
nop.m 0
nop.f 0
(p13) add GR_2xDx = GR_Dx,GR_Dx
};;
{ .mfi
nop.m 0
fma.s1 FR_A3 = FR_A4,FR_x,FR_A3
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_A1 = FR_A2,FR_x,FR_A1
(p13) cmp.leu.unc p10,p0 = GR_Root,GR_2xDx
};;
{ .mfi
nop.m 0
frcpa.s1 FR_InvX,p0 = f1,FR_Req
nop.i 0
}
{ .mfi
nop.m 0
(p10) fms.s1 FR_rx = FR_NormX,f1,FR_Root
nop.i 0
};;
{ .mfi
getf.exp GR_SignExp = FR_Req
fma.s1 FR_x4 = FR_x2,FR_x2,f0
nop.i 0
};;
{ .mfi
getf.sig GR_Sig = FR_Req
fma.s1 FR_A5 = FR_A7,FR_x2,FR_A5
nop.i 0
};;
{ .mfi
sub GR_PureExp = GR_SignExp,GR_ExpBias
fma.s1 FR_w2 = FR_w,FR_w,f0
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_Q32 = FR_P3,FR_w,FR_P2
nop.i 0
};;
{ .mfi
setf.sig FR_int_Ln = GR_PureExp
fma.s1 FR_A1 = FR_A3,FR_x2,FR_A1
extr.u GR_Ind4T = GR_Sig,55,8
}
{ .mfi
nop.m 0
fma.s1 FR_Q10 = FR_P1,FR_w,f1
nop.i 0
};;
{ .mfi
shladd GR_ad_T = GR_Ind4T,3,GR_ad_Data
fms.s1 FR_r = FR_InvX,FR_Req,f1
nop.i 0
}
{ .mfi
nop.m 0
(p10) fms.s1 FR_rx2 = FR_rx,FR_rx,f0
nop.i 0
};;
{ .mfi
ldfd FR_T = [GR_ad_T]
(p10) fma.s1 FR_R2 = FR_R3,FR_rx,FR_R2
nop.i 0
}
{ .mfi
nop.m 0
(p10) fma.s1 FR_R0 = FR_R1,FR_rx,FR_R0
nop.i 0
};;
{ .mfi
getf.exp GR_Exp = FR_w
fma.s1 FR_A1 = FR_A5,FR_x4,FR_A1
mov GR_ExpMask = 0x1ffff
}
{ .mfi
nop.m 0
fma.s1 FR_Q32 = FR_Q32, FR_w2,FR_Q10
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_r2 = FR_r,FR_r,f0
mov GR_fff7 = 0xFFF7
}
{ .mfi
nop.m 0
fma.s1 FR_P32 = FR_P3,FR_r,FR_P2
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_P10 = FR_P1,FR_r,f1
and GR_Exp = GR_ExpMask,GR_Exp
}
{ .mfb
nop.m 0
(p10) fma.s.s0 f8 = FR_R2,FR_rx2,FR_R0
(p10) br.ret.spnt b0 // exit for arguments close to negative roots
};;
{ .mfi
nop.m 0
fcvt.xf FR_N = FR_int_Ln
nop.i 0
}
{ .mfi
cmp.ge p14,p15 = GR_Exp,GR_fff7
nop.f 0
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_A0 = FR_A1,FR_x,FR_A0
nop.i 0
}
{ .mfi
nop.m 0
(p15) fma.s1 FR_Ln = FR_Q32,FR_w,f0
nop.i 0
};;
{ .mfi
nop.m 0
(p14) fma.s1 FR_P32 = FR_P32,FR_r2,FR_P10
cmp.eq p6,p7 = 0,GR_Ind
};;
{ .mfi
nop.m 0
(p14) fma.s1 FR_T = FR_N,FR_Ln2,FR_T
nop.i 0
};;
{ .mfi
nop.m 0
(p14) fma.s1 FR_Ln = FR_P32,FR_r,FR_T
nop.i 0
};;
.pred.rel "mutex",p6,p7
{ .mfi
nop.m 0
(p6) fms.s.s0 f8 = FR_A0,FR_x,FR_Ln
nop.i 0
}
{ .mfb
nop.m 0
(p7) fms.s.s0 f8 = FR_A0,f1,FR_Ln
br.ret.sptk b0
};;
// branch for calculating of ln(GAMMA(x)) for x < -2^13
//---------------------------------------------------------------------
.align 32
lgammaf_negstirling:
{ .mfi
shladd GR_ad_T = GR_Ind4T,3,GR_ad_Data
fms.s1 FR_Xf = FR_NormX,f1,FR_N // xf = x - [x]
mov GR_SingBound = 0x10016
}
{ .mfi
add GR_ad_Co = 0xCA0,GR_ad_Data
fma.s1 FR_P32 = FR_P3,FR_r,FR_P2
nop.i 0
};;
{ .mfi
ldfd FR_T = [GR_ad_T]
fcvt.xf FR_int_Ln = FR_int_Ln
cmp.le p6,p0 = GR_SingBound,GR_Exp
}
{ .mfb
add GR_ad_Ce = 0x20,GR_ad_Co
fma.s1 FR_r2 = FR_r,FR_r,f0
(p6) br.cond.spnt lgammaf_singularity
};;
{ .mfi
// load coefficients of polynomial approximation
// of ln(sin(Pi*xf)/(Pi*xf)), |xf| <= 0.5
ldfpd FR_S16,FR_S14 = [GR_ad_Co],16
fma.s1 FR_P10 = FR_P1,FR_r,f1
nop.i 0
}
{ .mfi
ldfpd FR_S12,FR_S10 = [GR_ad_Ce],16
fms.s1 FR_xm05 = FR_NormX,f1,FR_05
nop.i 0
};;
{ .mmi
ldfpd FR_S8,FR_S6 = [GR_ad_Co],16
ldfpd FR_S4,FR_S2 = [GR_ad_Ce],16
nop.i 0
};;
{ .mfi
getf.sig GR_N = FR_int_Ntrunc // signgam calculation
fma.s1 FR_Xf2 = FR_Xf,FR_Xf,f0
nop.i 0
};;
{ .mfi
nop.m 0
frcpa.s1 FR_InvXf,p0 = f1,FR_Xf
nop.i 0
};;
{ .mfi
getf.d GR_Arg = FR_Xf
fcmp.eq.s1 p6,p0 = FR_NormX,FR_N
mov GR_ExpBias = 0x3FF
};;
{ .mfi
nop.m 0
fma.s1 FR_T = FR_int_Ln,FR_Ln2,FR_T
extr.u GR_Exp = GR_Arg,52,11
}
{ .mfi
nop.m 0
fma.s1 FR_P32 = FR_P32,FR_r2,FR_P10
nop.i 0
};;
{ .mfi
sub GR_PureExp = GR_Exp,GR_ExpBias
fma.s1 FR_S14 = FR_S16,FR_Xf2,FR_S14
extr.u GR_Ind4T = GR_Arg,44,8
}
{ .mfb
mov GR_SignOfGamma = 1 // set signgam to -1
fma.s1 FR_S10 = FR_S12,FR_Xf2,FR_S10
(p6) br.cond.spnt lgammaf_singularity
};;
{ .mfi
setf.sig FR_int_Ln = GR_PureExp
fms.s1 FR_rf = FR_InvXf,FR_Xf,f1
// set p14 if GR_N is even
tbit.z p14,p0 = GR_N,0
}
{ .mfi
shladd GR_ad_T = GR_Ind4T,3,GR_ad_Data
fma.s1 FR_Xf4 = FR_Xf2,FR_Xf2,f0
nop.i 0
};;
{ .mfi
(p14) sub GR_SignOfGamma = r0,GR_SignOfGamma // set signgam to -1
fma.s1 FR_S6 = FR_S8,FR_Xf2,FR_S6
nop.i 0
}
{ .mfi
// set p9 if signgum is 32-bit int
// set p10 if signgum is 64-bit int
cmp.eq p10,p9 = 8,r34
fma.s1 FR_S2 = FR_S4,FR_Xf2,FR_S2
nop.i 0
};;
{ .mfi
ldfd FR_Tf = [GR_ad_T]
fma.s1 FR_Ln = FR_P32,FR_r,FR_T
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_LnSqrt2Pi = FR_LnSqrt2Pi,f1,FR_NormX
nop.i 0
};;
.pred.rel "mutex",p9,p10
{ .mfi
(p9) st4 [r33] = GR_SignOfGamma // as 32-bit int
fma.s1 FR_rf2 = FR_rf,FR_rf,f0
nop.i 0
}
{ .mfi
(p10) st8 [r33] = GR_SignOfGamma // as 64-bit int
fma.s1 FR_S10 = FR_S14,FR_Xf4,FR_S10
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_P32f = FR_P3,FR_rf,FR_P2
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_Xf8 = FR_Xf4,FR_Xf4,f0
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_P10f = FR_P1,FR_rf,f1
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_S2 = FR_S6,FR_Xf4,FR_S2
nop.i 0
};;
{ .mfi
nop.m 0
fms.s1 FR_Ln = FR_Ln,FR_xm05,FR_LnSqrt2Pi
nop.i 0
};;
{ .mfi
nop.m 0
fcvt.xf FR_Nf = FR_int_Ln
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_S2 = FR_S10,FR_Xf8,FR_S2
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_Tf = FR_Nf,FR_Ln2,FR_Tf
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_P32f = FR_P32f,FR_rf2,FR_P10f // ??????
nop.i 0
};;
{ .mfi
nop.m 0
fnma.s1 FR_Ln = FR_S2,FR_Xf2,FR_Ln
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_Lnf = FR_P32f,FR_rf,FR_Tf
nop.i 0
};;
{ .mfb
nop.m 0
fms.s.s0 f8 = FR_Ln,f1,FR_Lnf
br.ret.sptk b0
};;
// branch for calculating of ln(GAMMA(x)) for -2^13 < x < -9
//---------------------------------------------------------------------
.align 32
lgammaf_negpoly:
{ .mfi
getf.d GR_Arg = FR_Xf
frcpa.s1 FR_InvXf,p0 = f1,FR_Xf
mov GR_ExpBias = 0x3FF
}
{ .mfi
nop.m 0
fma.s1 FR_Xf2 = FR_Xf,FR_Xf,f0
nop.i 0
};;
{ .mfi
getf.sig GR_N = FR_int_Ntrunc
fcvt.xf FR_N = FR_int_Ln
mov GR_SignOfGamma = 1
}
{ .mfi
nop.m 0
fma.s1 FR_A9 = FR_A10,FR_x,FR_A9
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_P10 = FR_P1,FR_r,f1
extr.u GR_Exp = GR_Arg,52,11
}
{ .mfi
nop.m 0
fma.s1 FR_x4 = FR_x2,FR_x2,f0
nop.i 0
};;
{ .mfi
sub GR_PureExp = GR_Exp,GR_ExpBias
fma.s1 FR_A7 = FR_A8,FR_x,FR_A7
tbit.z p14,p0 = GR_N,0
}
{ .mfi
nop.m 0
fma.s1 FR_A5 = FR_A6,FR_x,FR_A5
nop.i 0
};;
{ .mfi
setf.sig FR_int_Ln = GR_PureExp
fma.s1 FR_A3 = FR_A4,FR_x,FR_A3
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_A1 = FR_A2,FR_x,FR_A1
(p14) sub GR_SignOfGamma = r0,GR_SignOfGamma
};;
{ .mfi
nop.m 0
fms.s1 FR_rf = FR_InvXf,FR_Xf,f1
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_Xf4 = FR_Xf2,FR_Xf2,f0
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_S14 = FR_S16,FR_Xf2,FR_S14
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_S10 = FR_S12,FR_Xf2,FR_S10
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_T = FR_N,FR_Ln2,FR_T
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_P32 = FR_P32,FR_r2,FR_P10
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_S6 = FR_S8,FR_Xf2,FR_S6
extr.u GR_Ind4T = GR_Arg,44,8
}
{ .mfi
nop.m 0
fma.s1 FR_S2 = FR_S4,FR_Xf2,FR_S2
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_A7 = FR_A9,FR_x2,FR_A7
nop.i 0
}
{ .mfi
shladd GR_ad_T = GR_Ind4T,3,GR_ad_Data
fma.s1 FR_A3 = FR_A5,FR_x2,FR_A3
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_Xf8 = FR_Xf4,FR_Xf4,f0
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_rf2 = FR_rf,FR_rf,f0
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_P32f = FR_P3,FR_rf,FR_P2
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_P10f = FR_P1,FR_rf,f1
nop.i 0
};;
{ .mfi
ldfd FR_Tf = [GR_ad_T]
fma.s1 FR_Ln = FR_P32,FR_r,FR_T
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_A0 = FR_A1,FR_x,FR_A0
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_S10 = FR_S14,FR_Xf4,FR_S10
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_S2 = FR_S6,FR_Xf4,FR_S2
nop.i 0
};;
{ .mfi
nop.m 0
fcvt.xf FR_Nf = FR_int_Ln
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_A3 = FR_A7,FR_x4,FR_A3
nop.i 0
};;
{ .mfi
nop.m 0
fcmp.eq.s1 p13,p0 = FR_NormX,FR_Ntrunc
nop.i 0
}
{ .mfi
nop.m 0
fnma.s1 FR_x3 = FR_x2,FR_x,f0 // -x^3
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_P32f = FR_P32f,FR_rf2,FR_P10f
nop.i 0
};;
{ .mfb
// set p9 if signgum is 32-bit int
// set p10 if signgum is 64-bit int
cmp.eq p10,p9 = 8,r34
fma.s1 FR_S2 = FR_S10,FR_Xf8,FR_S2
(p13) br.cond.spnt lgammaf_singularity
};;
.pred.rel "mutex",p9,p10
{ .mmf
(p9) st4 [r33] = GR_SignOfGamma // as 32-bit int
(p10) st8 [r33] = GR_SignOfGamma // as 64-bit int
fms.s1 FR_A0 = FR_A3,FR_x3,FR_A0 // -A3*x^3-A0
};;
{ .mfi
nop.m 0
fma.s1 FR_Tf = FR_Nf,FR_Ln2,FR_Tf
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_Ln = FR_S2,FR_Xf2,FR_Ln // S2*Xf^2+Ln
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_Lnf = FR_P32f,FR_rf,FR_Tf
nop.i 0
};;
{ .mfi
nop.m 0
fms.s1 FR_Ln = FR_A0,f1,FR_Ln
nop.i 0
};;
{ .mfb
nop.m 0
fms.s.s0 f8 = FR_Ln,f1,FR_Lnf
br.ret.sptk b0
};;
// branch for handling +/-0, NaT, QNaN, +/-INF and denormalised numbers
//---------------------------------------------------------------------
.align 32
lgammaf_spec:
{ .mfi
getf.exp GR_SignExp = FR_NormX
fclass.m p6,p0 = f8,0x21 // is arg +INF?
mov GR_SignOfGamma = 1 // set signgam to 1
};;
{ .mfi
getf.sig GR_Sig = FR_NormX
fclass.m p7,p0 = f8,0xB // is x deno?
// set p11 if signgum is 32-bit int
// set p12 if signgum is 64-bit int
cmp.eq p12,p11 = 8,r34
};;
.pred.rel "mutex",p11,p12
{ .mfi
// store sign of gamma(x) as 32-bit int
(p11) st4 [r33] = GR_SignOfGamma
fclass.m p8,p0 = f8,0x1C0 // is arg NaT or NaN?
dep.z GR_Ind = GR_SignExp,3,4
}
{ .mib
// store sign of gamma(x) as 64-bit int
(p12) st8 [r33] = GR_SignOfGamma
and GR_Exp = GR_ExpMask,GR_SignExp
(p6) br.ret.spnt b0 // exit for +INF
};;
{ .mfi
sub GR_PureExp = GR_Exp,GR_ExpBias
fclass.m p9,p0 = f8,0x22 // is arg -INF?
extr.u GR_Ind4T = GR_Sig,55,8
}
{ .mfb
nop.m 0
(p7) fma.s0 FR_tmp = f1,f1,f8
(p7) br.cond.sptk lgammaf_core
};;
{ .mfb
nop.m 0
(p8) fms.s.s0 f8 = f8,f1,f8
(p8) br.ret.spnt b0 // exit for NaT and NaN
};;
{ .mfb
nop.m 0
(p9) fmerge.s f8 = f1,f8
(p9) br.ret.spnt b0 // exit -INF
};;
// branch for handling negative integers and +/-0
//---------------------------------------------------------------------
.align 32
lgammaf_singularity:
{ .mfi
mov GR_SignOfGamma = 1 // set signgam to 1
fclass.m p6,p0 = f8,0x6 // is x -0?
mov GR_TAG = 109 // negative
}
{ .mfi
mov GR_ad_SignGam = r33
fma.s1 FR_X = f0,f0,f8
nop.i 0
};;
{ .mfi
nop.m 0
frcpa.s0 f8,p0 = f1,f0
// set p9 if signgum is 32-bit int
// set p10 if signgum is 64-bit int
cmp.eq p10,p9 = 8,r34
}
{ .mib
nop.m 0
(p6) sub GR_SignOfGamma = r0,GR_SignOfGamma
br.cond.sptk lgammaf_libm_err
};;
// overflow (x > OVERFLOV_BOUNDARY)
//---------------------------------------------------------------------
.align 32
lgammaf_overflow:
{ .mfi
nop.m 0
nop.f 0
mov r8 = 0x1FFFE
};;
{ .mfi
setf.exp f9 = r8
fmerge.s FR_X = f8,f8
mov GR_TAG = 108 // overflow
};;
{ .mfi
mov GR_ad_SignGam = r33
nop.f 0
// set p9 if signgum is 32-bit int
// set p10 if signgum is 64-bit int
cmp.eq p10,p9 = 8,r34
}
{ .mfi
nop.m 0
fma.s.s0 f8 = f9,f9,f0 // Set I,O and +INF result
nop.i 0
};;
// gate to __libm_error_support#
//---------------------------------------------------------------------
.align 32
lgammaf_libm_err:
{ .mmi
alloc r32 = ar.pfs,1,4,4,0
mov GR_Parameter_TAG = GR_TAG
nop.i 0
};;
.pred.rel "mutex",p9,p10
{ .mmi
// store sign of gamma(x) as 32-bit int
(p9) st4 [GR_ad_SignGam] = GR_SignOfGamma
// store sign of gamma(x) as 64-bit int
(p10) st8 [GR_ad_SignGam] = GR_SignOfGamma
nop.i 0
};;
GLOBAL_LIBM_END(__libm_lgammaf)
LOCAL_LIBM_ENTRY(__libm_error_region)
.prologue
{ .mfi
add GR_Parameter_Y=-32,sp // Parameter 2 value
nop.f 0
.save ar.pfs,GR_SAVE_PFS
mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
}
{ .mfi
.fframe 64
add sp=-64,sp // Create new stack
nop.f 0
mov GR_SAVE_GP=gp // Save gp
};;
{ .mmi
stfs [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack
add GR_Parameter_X = 16,sp // Parameter 1 address
.save b0, GR_SAVE_B0
mov GR_SAVE_B0=b0 // Save b0
};;
.body
{ .mib
stfs [GR_Parameter_X] = FR_X // STORE Parameter 1
// on stack
add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
nop.b 0
}
{ .mib
stfs [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3
// on stack
add GR_Parameter_Y = -16,GR_Parameter_Y
br.call.sptk b0=__libm_error_support# // Call error handling
// function
};;
{ .mmi
nop.m 0
nop.m 0
add GR_Parameter_RESULT = 48,sp
};;
{ .mmi
ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack
.restore sp
add sp = 64,sp // Restore stack pointer
mov b0 = GR_SAVE_B0 // Restore return address
};;
{ .mib
mov gp = GR_SAVE_GP // Restore gp
mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
br.ret.sptk b0 // Return
};;
LOCAL_LIBM_END(__libm_error_region)
.type __libm_error_support#,@function
.global __libm_error_support#
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